For my new project I chose to use "Business Directory Plugin" and "another-wordpress-classifieds-plugin" and adjust all things go, but there was a problem when I installed Social Gallery Plugin.
The problem is that Social Gallery Plugin lightbox opens before lightbox of other 2 modules and prevents them from opening. The instruction of Social Gallery Plugin says that you can choose only one class or div id individual and Social Gallery plugin only be opened for him. I tried it, but it did not

Sounds like you have a lightbox conflict. AWPCP and BD both have settings where you can disable the lightbox effect coming from them in that case. For BD, look under Directory Admin->Manage Options, Images tab. For AWPCP, look under Classifieds->Settings, Images. Each should have a checkbox regarding lightbox settings on there.